The magnitude of the scalar field, represented by the function \(f(r)\) , starts at zero at the origin \(r=0\)  and reaches its VEV asymptotically (at a large radius, the computational boundary \(R\)  which represents formally infinity). An important feature is that the scalar field reaches its VEV slower, over a larger radius, as one approaches the critical coupling \(\xi _c\) . In other words, the core of the vortex extends out further. The plot of the scalar field's “extension" The extension is defined here as the radius where it reaches \(99.9\%\)  of its VEV. as a function of \(\xi \)  shows a dramatic increase near the critical coupling \(\xi _c\) . We show analytically that the extension is expected to diverge in the limit \(\xi \rightarrow \xi _c\) . This is the analog to the divergence of the coherence length at the critical temperature \(T_c\)  in GL mean-field theory [1]}, [2]}. We also plot the extension of the magnetic field which shows a similar trend; starting at its peak value at the origin, it falls off slower (extends further out) as one approaches the critical coupling \(\xi _c\) .
